Sensor probe for measuring temperature and liquid volumetric fraction of a liquid droplet laden hot gas and method of using same

ABSTRACT

A sensor probe and method of use for determining the temperature, velocity, and/or liquid volumetric fraction of gas laden with droplets. In one variation, the probe includes a single heating element used in a well-characterized flow. The heating element is maintained above the Leidenfrost transition for the droplets, which prevents cooling effects from the droplets from impacting the temperature measurement. In another variation, the probe includes two or more heating elements arranged in similar flow environments. The property of interest is derived by relying on thermodynamic and heat transfer principles, which are not usable in conjunction with conventional devices. In one variation, the temperature is determined using a relationship function for characteristics of two heating elements, maintained at two different temperatures, along with the power needed to maintain constant temperature in each element, and by eliminating dependence on other variables for the determination, such as the velocity of the gas.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Division of application Ser. No. 10/103,561 filed Mar. 22,2002, now U.S. Pat. No. 6,609,412 which claims benefit of U.S.Provisional Application No. 60/277,772 filed Mar. 22, 2001. Thedisclosures of the prior applications are hereby incorporated byreference herein in their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to a wet gas probe. More particularly,this invention relates to a sensor probe capable of accurately measuringthe temperature and liquid volumetric fraction of a hot gas laden withliquid droplets.

2. Description of Related Art

For many liquids, there is a temperature well above the boiling pointcalled the Leidenfrost point or Leidenfrost transition. As an example,water has a Leidenfrost point of 300-350° C. at atmospheric conditions.Consider a simple experiment where a droplet of water is placed on asurface kept at a temperature above the boiling point of water. If thetemperature of the surface is below the Leidenfrost point, then thedroplet starts to spread out and vaporizes rather quickly.

However, if the temperature of the surface is at or above theLeidenfrost point, the bottom layer of the droplet vaporizes almostimmediately on contact, creating a cushion of vapor that repels the restof the droplet from the surface. Furthermore, the evaporation of thebottom layer of the droplet from the surface produces a cooling effect,which detrimentally affects the heating of the surface. The remainingportion of the droplet does not make contact with the surface, and thusno heat can be transferred directly from the surface to the droplet. Atsuch high temperatures, one might expect that the vapor layer wouldquickly transfer enough heat to the rest of the droplet to vaporize thedroplet. Water vapor, however, is a very poor conductor of heat at thesetemperatures. Hence, the vapor layer actually acts as an insulator.

Currently it is quite difficult to accurately measure gas temperature ina liquid droplet and gas mixture. Most common gas measurement devices,such as thermocouples and resistance temperature detectors (RTD), workon the principal that the electrical resistance of most materials varieswith temperature. Hence, knowledge of the functional relationshipbetween temperature and change in resistance of a given material(s) andmeasurement of this change allows for inference of the temperature ofthe gas stream. Generally, these devices are comprised of differentmetals, which have high thermal conductivity. In a liquid-droplet gasmixture, the droplets will tend to impact and coat the surface of thesedevices. The liquid on the surface of the probe draws heat from themeasurement device, in a process known as evaporative cooling. Thisprocess results in measurement of temperatures much below the true gastemperature. This phenomenon prevents these common temperaturemeasurement devices from accurately measuring gas temperature in thisenvironment. As described above, the invention eliminates this problemby preventing the droplet from impacting the surface of the probe bykeeping the measurement surface above the Leidenfrost point.

The above-identified phenomena give rise to an unsolved problem in theprior art of measuring the temperature and other characteristics ofgases laden with liquid droplets. The need to solve this problem arisesin a wide variety of contexts, including, for example, measurement ofgas temperature in propulsion and power generation systems, which oftenuse water or other liquid introduced into the system to, for example,control emissions (e.g., pollution control) or augment power. In suchapplications, determination and control of gas temperature may beimportant to performance. Many other systems, devices, and situationsarise, such as a gas turbine, combustion engine, tank, pipe, duct,manifold, chamber, or the like, as well as external flows, including,for example, droplets in an open air environment, in which the presenceof liquid droplets in a gas can produce difficulties in measuring gastemperature and other properties of the gas.

As an example, one simple conventional temperature and liquid sensitivesystem for which this problem can arise is a fire detection system, anexample of application of which is as follows. As is well known, firedetection systems are installed in residential and commercial buildingsto protect property and occupants from fire. An important characteristicof the fire detection system is the capability to detect a fire in theearly stages, when the fire is still small. Early detection andactivation by fire suppression devices are important to allow more timefor the evacuation of the occupants as well as to increase the chance ofsuccessfully suppressing the fire before extensive damage is caused tothe buildings. Therefore, the early detection of a fire is veryimportant.

Ceiling mounted devices that do not interfere with normal roomarrangements are generally preferred for fire protection purposes.Automatic sprinklers are devices that distribute water onto a fire insufficient quantity either to extinguish the fire in its entirety or toprevent the spread of the fire in case the fire is too far from thewater discharged by the sprinklers. Typically, the water is fed to thesprinklers through a system of piping, suspended from the ceiling, withthe sprinklers placed at regular intervals along the pipes. The orificeof the sprinkler head is normally closed by a disk or cap held in placeby a temperature sensitive releasing element. The temperature sensitivereleasing element of the sprinkler will be referred to hereinafter as asprinkler link.

Automatic sprinklers have several temperature ratings that are based onstandardized tests in which a sprinkler is immersed in a liquid and thetemperature of the liquid raised very slowly until the sprinkleractivates. The temperature rating of most automatic sprinklers isstamped on the sprinkler. The time delay between the onset of the fireand the activation of the sprinkler depends upon several parameters,such as the placement of the sprinkler with respect to the fire, thedimensions of the enclosed space, the energy generated by the combustionand the sensitivity of the sprinkler.

Buoyancy pushes the hot products generated by a fire toward the ceilingwhile mixing with room air to form a hot-gas plume. Impingement of thehot-gas plume on the ceiling results in a gas flow near the ceiling,even at a considerable distance from the core of the fire. This flow isresponsible for directing hot gases to the thermally actuated firedetection devices.

The rate of heat released by the fire and the room dimensions are themain parameters of considerable importance in any discussion offire-induced convection near the room ceiling. Also, the size and thecomposition of the sprinkler link influences the sensitivity of thesprinkler. Other conditions being equal, the sensitivity of a sprinkleris inversely proportional to the time required for the sprinkler link tomelt. Therefore, sprinklers are rated according to their Response TimeIndex, hereinafter referred to as RTI, which characterizes the speed ofthe sprinklers response to a fire.

The RTI is the product of the thermal time constant of the sprinklerlink and the square root of the flow velocity of the hot gas. Thisparameter is reasonably constant for any given sprinkler and isconsidered sufficient for predicting the sprinkler response for knowngas temperatures and velocities near the sprinkler. However, recentfull-scale tests on warehouse fires uncovered a behavior of sprinklersthat does not correspond to the predictions of the RTI model.

The RTI model considers the sprinkler link as a cylinder in cross-flow.It is assumed that the heat transfer between the hot gases flowing underthe ceiling and the sprinkler is convective and radiative, thus, amongother factors, the RTI model neglects the presence of water droplets inthe airflow.

The first sprinkler to activate in case of fire is referred to as aprimary sprinkler and the surrounding sprinklers are identified assecondary sprinklers. Tests show that the primary sprinkler activates aspredicted, but the secondary sprinklers respond after a much longerdelay than suggested by the RTI model. In some cases, the sprinklersimmediately surrounding the primary sprinkler do not activate at all,whereas the sprinklers farther away do activate.

Such observations may be explained in part by considering the presenceof water droplets in the hot gas plume following the activation of theprimary sprinkler. Some of the water droplets sprayed by the primarysprinkler do not reach the ground but are entrained and carried away bythe ascending plume. Most of these water droplets evaporate inside theplume, while a small fraction of the remaining water droplets travel farenough to reach and impact the secondary sprinklers. The subsequentevaporation of the water droplets from the sprinkler link surface of thesecondary sprinklers produces a cooling effect, which delays the heatingof the sprinkler link. The delay in the heating of the sprinkler linkresults in a delay in the activation of the sprinkler which cannot bepredicted by the RTI model.

There remains an unmet need to solve the problem of measurement of thecharacteristics, including gas temperature, for hot gases containingliquid droplets in a wide range of environments and applications.

SUMMARY OF THE INVENTION

The present invention solves these and other problems of the prior artby providing a sensor probe and method of use for determining thetemperature and liquid volumetric fraction of a hot gas laden withliquid droplets in a wide range of applications. In one embodiment, asingle heating element is used in a well-characterized, droplet-ladenflow. The heating element is maintained above the Leidenfrost transitionfor the droplets which prevents cooling effects from the droplets fromimpacting the temperature measurement. In this embodiment, the heat lossfrom the probe is determined by the power needed to maintain a constanttemperature in the element and the convective heat transfer coefficientis determined by calibration in the well-characterized flow or fromfundamental properties of the well-characterized flow. Specifically, ifthe Reynolds number (Re) and the Prandtl number (Pr) of the flow areknown, the convective heat transfer coefficient can be calculated fromthe Nusselt (Nu) number by a person skilled in the art. Similarly, ifthe temperature of the flow is known, the velocity of the flow can bedetermined through the velocity dependence of the convective heattransfer coefficient by calibration or from fundamental properties ofthe fluid. Such determination can include, but is not limited to, use ofa processor, such as a personal computer, minicomputer, main framecomputer, or microcomputer.

In another embodiment of the present invention, the heating elements arearranged so as to be in similar flow environments, such as by beingarranged parallel, coplanar, or coaxial to one another. For example, ina single direction flow environment, the heating elements may bearranged coaxial to one another, perpendicular to the direction of flow.At least two heating elements are maintained at a temperature above theLeidenfrost transition for the liquid droplets (e.g., the Leidenfrosttransition for water droplets is in a range between 300-350° C. atatmospheric conditions; other liquids have determinable Leidenfrosttransition temperature ranges), which prevents cooling effects of thedroplets from impacting the temperature measurement. The gas temperatureis derived by relying on thermodynamic and heat transfer principles,which are not usable in conjunction with conventional devices (e.g.,devices designed for use at below Leidenfrost transition temperaturesand for which the presence of liquid droplets impacts performance). Inone variation, the temperature is determined using a relationshipfunction for characteristics of two heating elements, maintained at twodifferent temperatures, and the power needed to maintain a constanttemperature in each element, and by eliminating dependence on othervariables for the determination, such as the velocity of the gas, oneimportant factor is heat loss from the heating elements.

More specifically, in an embodiment of the present invention, atemperature of the hot gas laden within liquid droplets is determinedbased on characteristics of heating elements in the hot gas and liquiddroplet environment, such as by using a derived relationship functionfor the first and second temperatures of first and second heatingelements positioned so as to be in a similar flow environment. Heat lossfor the two elements is usable in this embodiment to determine gasproperties, such as gas temperature. Heat loss can be measured in manyways. For example, if the heating elements are maintained at a constanttemperature using a power source, heat loss varies as a function of thepower supplied to each element, and the ratio of power supplied to thefirst and second heating elements by the controller is usable todetermine relative heat loss, and from this information, gas temperaturecan be determined. As the derived relationship function eliminatesvariables for gas velocity, the determination of temperature is notaffected by the velocity of the hot gas flow, and as the heatingelements are both maintained above the Leidenfrost point for the liquidpresent in the hot gas, the presence of the liquid droplets in the hotgas flow likewise does not affect temperature determination.

In one embodiment of the present invention, heat loss is determinedbased on the power needed to maintain each heating element at apredetermined temperature, with the heat loss of the first and secondheating elements and ratio of power supplied to the first and secondheating elements being used to determine the temperature of the hot gasladen with liquid droplets, based on the relationship of T_(G)=A·w+B,where T_(G) is the temperature of the hot gas, A and B are numericalconstants having values dependent upon the configuration of the sensorprobes, and w is the ratio of an electrical resistance across the secondheating element at the second temperature to an electrical resistanceacross a resistor that is in series with the second heating element.

According to yet another aspect of the invention, a liquid volumetricfraction of the hot gas laden with liquid droplets is determinable usinginformation obtained from one or more of the heat elements andinformation obtained from a wetted sensor. In one embodiment, the liquidvolumetric fraction of the hot gas is determined based on therelationship of β=(0.012±0.001)(T_(G)−T_(W))/(U·D)1/2, where βrepresents the liquid volumetric fraction, T_(G) is the temperature ofthe hot gas laden with liquid droplets, T_(W) is a temperature measuredby a wetted sensor, U is the velocity of the hot gas laden with liquiddroplets, and D is the outer diameter of the wetted sensor.

In one embodiment of the present invention, the controller controls theoperation parameters of the first and second heating elementssimultaneously (i.e., at the same time), using, for example, a circuitcontaining a Wheatstone bridge.

In an embodiment of the present invention, the sensor includes at leasttwo heating elements connected to insulating rods attached to a supportframe. A controller is connected to the support frame and controls theoperation parameters of each of the heating elements, including thetemperature of the heating elements. The first heating element isconfigured to be maintained at a first temperature and the secondheating element is configured to be maintained at a second temperaturethat is less than the first temperature. The first and secondtemperatures are both above a Leidenfrost transition temperature atatmospheric conditions for the liquid present in the gas.

In an embodiment of the present invention, the first and second heatingelements may be any of a wide variety of shapes, including cylindrical,spherical, or having a rectangular or trapezoidal cross-section, and maybe, effectively, one, two, or three dimensional structures.

In one embodiment of the present invention for use in generally singledirectional gas flow applications, the first and second heating elementsare arranged to be parallel relative to each other. An insulator isconnected to each of the first and second heating elements that may becomprised of a rigid ceramic assembly. In another embodiment of thepresent invention for generally single directional gas flowapplications, the first and second heating elements are arranged to becoaxial relative to each other. In this embodiment, a support frame isused that includes three bent rods connected at a first end of each rodand equidistant from each other at a second end of each rod. The secondends of the rods are provided on a line coaxial with the longitudinalaxes of the first and second heating elements. A distance between thesecond ends of the rods is then equal to the length of the first andsecond heating elements.

A wide range of other configurations of the first and second heatingelements are also usable in conjunction with the present invention, solong as each element is positioned in a similar flow environment (e.g.,so that similar convective heat transfer error occurs for each element).

In an embodiment of the present invention, a connector may connect thefirst and second heating elements to the second ends of the rods. Theconnector may comprise a bore formed in the second end of each rod and afastener having a threaded portion and a head portion. The bore can besized and configured to receive the threaded portion of the fastener andthe head portion of the fastener maintains the heating element againstthe corresponding rod. The fastener may also include a clamp having abore identical to the bore in the second end of each rod and a terminalthat maintains a predetermined distance between the clamp and rod. Thebores can be sized and configured to receive the threaded portion of thefastener and the clamp maintains the heating element against thecorresponding rod.

According to yet another aspect of the invention, the first and secondheating elements may comprise a platinum wire. Furthermore, the supportframe and connecting rods can be enclosed within temperature-shrinkingtubing.

In another aspect of the invention, a method of measuringcharacteristics of a hot gas laden with liquid droplets uses a sensorprobe having at least two heating elements. In one embodiment, eachheating element is connected in series with an insulator and a supportframe, and the insulator connected to each heating element is, in turn,connected to a support frame. A controller controls the temperature ofeach of the heating elements. A first heating element is configured tobe maintained at a first temperature and a second heating element isconfigured to be maintained at a second temperature that is less thanthe first temperature, with both the first temperature and the secondtemperature being above the Leidenfrost temperature for the liquidpresent in the gas.

The method includes positioning the first and second heating elements ina flow of hot gas laden with liquid droplets, the elements beingpositioned in a similar flow environment, such as placement in parallelor coaxial, and orthogonal to the direction of the hot gas if the gashas a generally single flow direction. In one embodiment, power is thensupplied from the controller to the first and second heating elementsand the first and second temperatures are maintained above a Leidenfrosttransition temperature for the liquid at atmospheric conditions. Atemperature of the hot gas laden within liquid droplets is thendetermined, based on a relationship between a function of the first andsecond temperatures of the first and second heating elements and thepower supplied to the first and second heating elements.

According to another aspect of the invention, the method also includesdetermining the temperature of the hot gas laden with liquid dropletsbased on the relationship of T_(G)=A·w+B, where T_(G) is the temperatureof the hot gas, A and B are numerical constants having values dependentupon the configuration of the sensor probe, and w is the ratio of anelectrical resistance across the second heating element at the secondtemperature and an electrical resistance across a resistor in serieswith the second heating element.

According to another aspect of the invention, the method also includesdetermining a liquid volumetric fraction of the hot gas laden based onthe relationship of β=(0.012±0.001)(T_(G)−T_(W))/(U·D)1/2, where βrepresents a liquid volumetric fraction, T_(G) is a temperature of thehot gas laden with liquid droplets, T_(W) is a temperature measured by awetted sensor, U is a velocity of the hot gas laden with liquiddroplets, and D is an outer diameter of the wetted sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and advantages of the present invention willbecome more fully apparent from the following detailed description whenread in conjunction with the accompanying drawings with like referencenumerals indicating corresponding parts throughout, wherein:

FIG. 1 is a schematic drawing indicating the positioning of an examplesensor probe in the center of a test section, in accordance with anembodiment of the present invention;

FIG. 2 shows a dual heating element sensor probe according to a firstembodiment of the invention;

FIG. 3 shows a dual heating element sensor probe according to a secondembodiment of the invention;

FIG. 4 illustrates an example of how the heating elements of the sensorprobe are attached to rods;

FIG. 5 illustrates a schematic diagram of a wiring circuit used by thecontrol means for simultaneously controlling both heating elements;

FIG. 6 is a graph illustrating the change in temperature of each heatingelement relative to the change in the gas temperature;

FIG. 7 is a graph illustrating the results of a series of tests usingthe sensor probe of the present invention compared with using athermocouple under dry conditions;

FIG. 8 is a graph illustrating the results of a series of tests usingthe sensor probe of the present invention compared with the resultsobtained using the independent measurement system shown in FIGS. 10-13;

FIG. 9 is a graph illustrating the change in temperature of the hot andcold heating elements of the sensor probe according to the presentinvention compared to the change in gas temperature;

FIG. 10 is a schematic diagram of a once through circuit duct system ofan independent measurement system in which a hot gas flow is establishedto measure the response of a sensor probe according to this invention;

FIG. 11 is a schematic diagram showing the uniform flow of hot gaspassing through a finely atomized liquid spray after passing through ahoneycomb structure of the system shown in FIG. 10;

FIG. 12 illustrates the location of the vena contracta and test sectionin the duct system shown in FIG. 10;

FIG. 13 is a graph illustrating temperature distribution for dry and wetconditions;

FIG. 14 illustrates an alternate manner of connecting the heatingelements of the sensor probe to the rods of the sensor probe.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides a sensor probe and method of use fordetermining the temperature and liquid volumetric fraction of a hot gasladen with liquid droplets in a wide range of applications. In oneembodiment, a single heating element is used in a well-characterized,droplet-laden flow. The heating element is maintained above theLeidenfrost transition for the droplets which prevents cooling effectsfrom the droplets from impacting the temperature measurement. In thisembodiment, the heat loss from the probe is determined by the powerneeded to maintain a constant temperature in the element and theconvective heat transfer coefficient is determined by calibration in thewell-characterized flow or from fundamental properties of thewell-characterized flow. Specifically, if the Reynolds number (Re) andthe Prandtl number (Pr) of the flow are known, the convective heattransfer coefficient can be calculated from the Nusselt (Nu) number by aperson skilled in the art. Similarly, if the temperature of the flow isknown, the velocity of the flow can be determined through the velocitydependence of the convective heat transfer coefficient by calibration orfrom fundamental properties of the fluid. Such determination caninclude, but is not limited to, use of a processor, such as a personalcomputer, minicomputer, main frame computer, or microcomputer.

In another embodiment of the present invention, the probe includes twoor more heating elements arranged so as to be in similar flowenvironments. The two heating elements are maintained at a temperatureabove the Leidenfrost transition for the liquid droplets, which preventscooling effects of the droplets from impacting the temperaturemeasurement. The gas temperature is derived by relying on thermodynamicand heat transfer principles, which are not usable in conjunction withconventional devices (e.g., devices designed for use at belowLeidenfrost transition temperatures). In one variation, the temperatureis determined using a relationship function for characteristics of twoheating elements, maintained at two different temperatures, along withthe power needed to maintain a constant temperature in each element, andby eliminating dependence on other variables for the determination, suchas the velocity of the gas.

Analysis of data for conventional measurement techniques andconsideration of the properties of hot gas and liquid droplets areuseful in identifying relationships among probes that allowdetermination of temperature and other characteristics of hot gasescontaining liquid droplets. Conventional measurement of gas temperaturein wet and dry conditions and some properties of the gas and liquiddroplets, as well as devices relating to such measurement is describedfurther below in conjunction with FIGS. 10-13.

Turning now to the invention of this application, two temperatureproperties can be measured in a hot gas laden with liquid droplets,using two or more probes, which are referred to herein as cold and hotheating elements. The relationship between the temperature properties isusable to determine the gas temperature, as will be explained furtherbelow.

From Newton's law of convection, the following can be written for thecold and hot heating elements, respectively:

Q _(H) =h _(H) ·S·(T _(H) ·T _(G))  (1)

Q _(C) =h _(C) ·S·(T _(C) −T _(G))  (2)

Dividing Equation (1) by Equation (2) (note that Q_(C) is alwaysdifferent from zero since the temperature of cold heating element isgreater than any contemplated gas temperature), results in the followingexpression: $\begin{matrix}{\frac{Q_{H}}{Q_{C}} = {\frac{h_{H}}{h_{C}} \cdot \frac{T_{H} - T_{G}}{T_{C} - T_{G}}}} & (3)\end{matrix}$

Although Equation (3) is theoretically correct, it does not match verywell with preliminary test results gathered from actual experiments,most likely due to the fact that convection is not the only heattransfer mechanism involved in the measurement, though the mostsignificant.

The gas temperature is obtained by considering the relationships amongthe hot heating element temperature T_(H) and its power Q_(H), the coldheating element temperature T_(C) and its power Q_(C), and the actualgas temperature T_(G), which corresponds to zero heating element power.

From these three conditions and again from the expressions of heattransfer, the following relationship is obtained for air laden withliquid droplets: $\begin{matrix}{\frac{T_{H} - T_{G}}{T_{C} - T_{G}} = {F \cdot ( \frac{Q_{H}}{Q_{C}} )^{b}}} & (4)\end{matrix}$

where F is a coefficient that depends on the ratio of the heat transfercoefficients.

Experimental tests performed at gas temperatures ranging between 100 and250° C. have shown that the value of F is very close to 0.9. Theexponent b would be expected to be almost equal to unity if the heattransfer mechanism were only convective. In such a case, Equation (4)reduces to Equation (3). But, since it is believed that radiation couldplay a small, but not negligible, role in this configuration, theexponent b is introduced as a parameter in Equation (4). The exponent bhas been experimentally found to be indeed smaller than one in someapplications, due to the relation between the heat flux dissipated bythe heating element and the temperature of the heating element itself.However, the effect of radiation can be eliminated in some cases by, forexample, using a different orientation of the heating elements.

In Equation (4), the hot and cold heating element temperatures, T_(H)and T_(C), are known because they are set by the operator andelectronically controlled by, for example, a controller. The powersQ_(H) and Q_(C) are easily obtained from the formula Q=i2 R (assumingpower is provided via an electrical circuit), where i is the quadraticmean value of the current flowing into the heating element and R is theresistance of the heating element. The resistance of each heatingelement is measured by changing the temperature in a predeterminedrange, such as 100-900° C., and performing a measurement at intervals,such as every 100° C. For example, the analysis of the experimental datamay show that the resistance according to an embodiment of the presentinvention using example heating elements produces an average resistancevalue of 112 Ω and ranges from 100 Ω at 100° C. to 124 Ω at 900° C. Thecurrent i is measured with appropriate instrumentation readily availablein the market.

Therefore, Equation (4) can be rearranged in the following way:$\begin{matrix}{\frac{T_{H} - T_{G}}{T_{C} - T_{G}} = {{F( \frac{i_{H}^{2} \cdot R_{H}}{i_{C}^{2} \cdot R_{C}} )}^{b} = {{F \cdot ( \frac{R_{H}}{R_{C}} )^{b}}( \frac{i_{H}}{i_{C}} )^{2b}}}} & (5)\end{matrix}$

The quantities F′ and b′ may be defined as follows: $\begin{matrix}{{F^{\prime} = {F \cdot ( \frac{R_{H}}{R_{C}} )^{b}}}{b^{\prime} = {2b}}} & \text{(6,7)}\end{matrix}$

It is thus possible to rewrite Equation (4) in a substantially similarway: $\begin{matrix}{\frac{T_{H} - T_{G}}{T_{C} - T_{G}} = {F^{\prime}( \frac{i_{H}}{i_{C}} )}^{b^{\prime}}} & (8)\end{matrix}$

Since the resistance of the heating elements increases with thetemperature (assuming an electrical circuit for the heating elements),the ratio RH/RC is somewhat larger than the unity. This implies that F′is even closer to the unity than F, thus simplifying considerably theanalysis of the data.

Several experiments were performed using the first embodiment of thesensor probe and Equation (8). A series of tests were used to evaluatethe coefficient F′ and b′ wherein it was found that F′≈0.9 and b′≈1.7.

The heating elements of the sensor probe output a heat power Q, whichobeys the Newton's law of convection. Therefore, one can obtain theconvective heat transfer by dividing the heat power Q by a product ofthe surface area of the heating element and the temperature differencebetween the heating element and gas. The velocity is then obtainedthrough correlations for the Nusselt number versus the availableReynolds number.

Use of these relationships for determining gas temperature will now bedemonstrated using an example application of the present invention in asimple gas flow environment. It will be readily apparent to thoseskilled in the art that other techniques for measuring heat loss forsensors maintained above the Leidenfrost temperature may be used inconjunction with the present invention, and that gas temperature andother properties may be similarly determined in many other, more complexenvironments, so long, for example, as each of the probes is located ina similar flow environment or accounting is made for differences in flowenvironment.

FIG. 1 is a schematic drawing indicating the positioning of an examplesensor probe 150, in accordance with an embodiment of the presentinvention, located in the center of a test section 100. In theillustrated embodiment, the sensor probe 150 is cylindrical, however, itis within the scope of this invention to have the sensor probe be anysuitable geometry, such as spherical, oblong, oval, box-shaped,rectangular, square, trapezoidal, pyramid shaped, as well as a plate ora disc shape, or a shape of a wire.

In the illustrated exemplary embodiment of FIG. 1, the sensor probe 150includes a heating element 152 placed in series with a rigid insulator154, preferably made of ceramic, which minimizes heat losses to asupport 156 connected thereto.

It should be noted that reference number 152 is used when discussing thecharacteristics and features of the heating elements in general and theheating elements are identified as having subscripts H and C whendiscussing the particular features or relationships of and between, forexample only, a hot temperature heating element 152 _(H) and a coldtemperature heating element 152 _(C).

The gas temperature T_(G) is obtained based on the measurements of twoheating elements 152 _(H) and 152 _(C) maintained at a hot temperatureand a cold temperature T_(H) and T_(C), respectively, by a controller200. The hot and cold temperatures T_(H) and T_(C) of the heatingelements 152 _(H) and 152 _(C) are above the Leidenfrost transition andthus unaffected by the liquid droplets present in the hot gas flow. Forpurposes of this example only, water was the liquid forming thedroplets. Calculations reveal the temperature of the gas T_(G) is afunction of the hot and cold temperatures T_(H) and T_(C) of the heatingelements 152 _(H) and 152 _(C), respectively, and the ratio of the powersupplied thereto by the controller 200.

To demonstrate the concept, consider a heating element 152 immersed in agas kept at constant temperature and flowing at constant velocity overthe heating element. The measurement of the power supplied thereto is afunction of the temperature of the heating element 152. In dryconditions, the power supply from the controller 200 is linearlyproportional to the temperature. This is under the assumption that theheat transfer coefficient does not change significantly with thetemperature of the heating element 152 and that the temperature of theheating element 152 is not too high such that the radiative contributioncan be neglected.

When liquid droplets are present, the linear dependence is accurate ifthe temperature of the heating element 152 is above the Leidenfrosttransition. For liquid water in this example, the transition occursapproximately at 300-350° C. at atmospheric conditions. The powerdissipated by the heating element 152 under wet conditions deviates fromthe linear behavior below that temperature because the heating element152 can also supply the energy to vaporize the water droplets depositedon its surface.

It should be noted that recent studies indicate that neither thevelocity of the liquid droplets nor the impact frequency of liquiddroplets over a hot surface significantly influence the Leidenfrosttransition.

FIG. 2 illustrates one embodiment of the dual heating element sensorprobe 150 of the present invention. The sensor probe 150 of thisembodiment is designed to measure the temperature of a one-dimensionalstream of hot gas with a velocity orthogonal to a plane of the probehaving the longitudinal axes L of the two heating elements 152 _(H) and152 _(C). Whether the sensor probe 150 is of this or another geometricconfiguration, the critical requirement is that it is placed so thateach heating element is located in a similar flow environment.

The heating elements 152 are controlled, preferably at the same time(i.e., simultaneously) by the controller 200. It should be noted thatthe specific details of the controller 200 are not relevant to anunderstanding of this invention. Rather, in this embodiment, thecontroller 200 need only be able to maintain the two heating elements152 _(H) and 152 _(C) at different temperatures, that is, a hottemperature T_(H) and a cold temperature T_(C), respectively, whereT_(H)>T_(C).

As indicated above, the heating elements 152 _(H) and 152 _(C) used inthe first embodiment of the sensor probe 150 output a heat power Q,which obeys the Newton's law of convection. Therefore, one can obtainthe convective heat transfer by dividing the heat power Q by a productof the surface area of the heating element 152 and the temperaturedifference between the heating element and gas. The velocity of the gasis then obtained through correlations for the Nusselt number versus theavailable Reynolds number. For a 9.3 mm diameter cylinder in cross-flow,the Reynolds number ranges from 600 to 2000. The heating element 152 ismaintained at a relatively low temperature, such as, for example, 400°C., to avoid significant heat transfer by radiation.

A second embodiment of the sensor probe 250 includes a smaller size ofthe two heating elements 252 _(H) (252) and 252 _(C) (252) andsignificantly improves the operation of the sensor probe 250 and reducesthe amount of error in the measurement. In particular, by rearrangingthe two heating elements 252 _(H) and 252 _(C) to be coaxial or in-lineeliminates any radiative heat transfer between the two heating elements.Furthermore, reducing the diameter of the heating elements 252 _(H) and252 _(C) lowers the heat transfer to the surroundings.

The lower heat transfer to the surroundings by the heating elements 252_(H) and 252 _(C) of this second embodiment is because the radiativeheat power Q_(rad) depends linearly on the diameter of the heatingelements 252 and the convective heat power Q_(conv) depends on thesquare root of the diameter. Hence, the convective heat transfer willdecrease less than the radiative heat transfer if a smaller diameter ofthe heating elements 252 is used.

The second embodiment of the sensor probe 250 results in a more flexibleand effective geometry that enables measurement of gas temperature forflows orthogonal to the longitudinal axis LL of the sensor probe.Furthermore, the approach of the gas flow to the sensor probe 250 can befrom anywhere within 360° of a plane orthogonal to longitudinal axis LLof the heating elements 252 _(H) and 252 _(C). Also, the diameter of theheating elements 252 is reduced to 0.2 mm.

The second embodiment of the sensor probe 250 provides many otheradvantages. For example, the elimination of heating element-to-heatingelement radiative exchanges that are present in the first embodiment.Also, the influence of the liquid droplets over the heat transferbetween cylindrical outer surface and the hot gas is reduced. Theradiative heat transfer to the suroundings is also reduced. Furthermore,the response time of the sensor probe 250 is reduced from severalminutes for the first embodiment to a few seconds for the secondembodiment.

As shown in FIG. 3, the sensor probe 250 according to the secondembodiment preferably includes a support frame 260 and a pair ofidentical heating elements 252 _(H) and 252 _(C) (252). The supportframe 260 includes three rods 254, preferably made from copper, that arecurved and joined at a first end 254 a wherein the rods 254 areequidistant from each other at a second end 254 b. The spacing betweenthe second ends 254 b of the rods 254 is equal to the length of theheating elements 252, which, in the embodiment illustrated in FIG. 3 arepreferably made of 0.2 mm diameter platinum wire having a length ofapproximately 30 mm. However, as stated above, the sensor probes 150 and250 may be of any suitable geometric configuration, such as a sphere,disc, rectangle, and the like. Therefore, the spacing between the secondends 254 b of the rods 254 should be able to receive and holdtherebetween two identical heating elements, regardless of the geometricconfiguration of the heating elements.

In the exemplary embodiment illustrated in FIG. 3, in order to havenegligible electrical resistance between the two heating elements 252_(H) and 252 _(C), which comprise platinum wires, respectively, the rods254 should have a rather large diameter, such as, for example only, 6.4mm. It should be understood that the diameter of the rods 254 willchange depending on the material, geometric configuration, size, length,diameter, and other such relevant characteristics of the material chosento comprise the heating elements 252. Preferably, temperature-shrinkingtubing 255 could be used to insulate the rods 254 from each other.

In embodiments of the present invention, the heating elements 252 areattached to the second ends 254 b of the three rods 254. FIG. 4illustrates one example of how the heating elements 252 can be attachedto the rods 254. For example, each rod 254 could have a bore 270 formedtherein that is sized and configured to receive a fastening device 271,which is shown as a screw, but can be any known or later developedsuitable fastening device. When the threaded portion 271 b of thefastening device 271 is threadably inserted into the bore 270 of the rod254, the head portion 271 a of the fastening device 271 would clamp theheating element 252 between a bottom surface of the head portion 271 aand the body of the rod 254.

FIG. 5 illustrates a schematic diagram of a wiring circuit that can beused by the controller 200 for simultaneously controlling both of theheating elements 252 _(H) and 252 _(C). Resistor element BS, shown inthe close up A of FIG. 5, is provided in the circuit since the heatingelements 252 _(H) and 252 _(C) are maintained at different temperatures(i.e., T_(H) and T_(C), where T_(H)>T_(C)). As such, each component ofthe circuit has constant resistance except for the heating elements 252.The resistance of the overall equivalent resistor element B, whichrepresents resistor element BS, shown in close up A, is maintainedconstant by varying the current flowing into the bridge and the voltageat the top of the bridge. Theory suggests that the resistance of elementB is constant when the difference of voltage between point E and F iszero, since the resistance of the components on the other legs of thebridge is constant.

Presuming the bridge is balanced, points E and F are at the same voltageand the power transistor supplies only the current necessary to theheating elements 252 _(H) and 252 _(C) to maintain their respectivetemperatures. An operational amplifier monitors the voltage differencebetween point F and point E, ΔV_(EF). If a change in the gas temperatureor gas velocity occurs, the operational amplifier outputs a signal V_(O)proportional to the difference of voltage ΔV_(EF). The power transistorreacts to the signal V_(O) by generating enough current to reach a newequilibrium point. Hence, the control circuit maintains the resistanceof element B constant, whatever the boundary conditions are, at leastwithin the power capabilities of the power transistor and the powerrating of the resistors in the circuit.

FIG. 6 illustrates the change in temperature of each heating element 252_(H) and 252 _(C) relative to the change in the gas temperature. Theresulting temperature of the cold heating element 252 _(C) is betweenthe temperature of the hot heating element 252 _(H) and the gastemperature because the power ratio for the two heating elements 252_(H) and 252 _(C) remains nearly constant. This is a rather significantfeature since the ratio of the heat transfer coefficients for the twoheating elements 252 _(H) and 252 _(C) is nearly constant over a widerange of gas temperatures. Further, by keeping the temperature of thecold heating element 252 _(C) equally distant from the temperature ofthe hot heating element 252 _(H) and the gas temperature, optimalaccuracy in sensor probe 250 measurements is achieved.

In the exemplary second embodiment, the two identical heating elements252 _(H) and 252 _(C) comprised of platinum wire are kept above theLeidenfrost transition, at different temperatures from each other, i.e.,T_(H) and T_(C), where T_(H)>T_(C). The energy balance for each platinumwire can be written as: $\begin{matrix}{\frac{\Delta \quad V^{2}}{R} = {h \cdot S \cdot ( {T - T_{G}} )}} & (9)\end{matrix}$

The arrangement for controlling a double wire component, element B inFIG. 9, is basically a Wheatstone bridge, with an operational amplifierhaving an output that is proportional to the voltage difference betweenpoints E and F. The operational amplifier controls a bipolar gate powertransistor so that the ratio of the resistances on the left side of thebridge is constantly equal to the ratio of the resistances on the rightside of the bridge. By ensuring that there is no voltage differencebetween points E and F, the control means 200 maintains the overallresistance of the leg EG to a set value chosen identical to theresistance R_(U). Also, the resistance of the element BS is chosen equalto R_(U). To this effect, any control device able to maintain theresistance EG at the constant value R_(U) is suitable for the operationand control of the probe. Introducing the variable w as the ratio of thevoltages across the cold heating element 252 _(C) and the resistorelement BS, one obtains: $\begin{matrix}{\frac{\Delta \quad V_{C}}{\Delta \quad V_{BS}} = {\frac{R_{C}}{R_{U}} = w}} & (10)\end{matrix}$

The electrical resistance of a platinum wire is a linear function of itstemperature, R=α·T+γ. If T is measured in Celsius degrees, thecoefficients α and γ are given respectively by:

α=0.003927·R ₂₀ ·L(OHM/° C.)  (11)

γ=R ₂₀ ·L−20·a (OHM)  (12)

where L is the length of the wire expressed in cm and R₂₀ is theresistance of platinum per unit length of wire, expressed in ohm/cm, at20° C. R₂₀ depends only on the diameter of the wire. Hence, Equation(10) becomes: $\begin{matrix}{\frac{{\alpha \quad T_{C}} + \gamma}{R_{U}} = w} & (13)\end{matrix}$

Solving Equation (13) with respect to the temperature of the coldheating element 252_(C), the following relationship is obtained:$\begin{matrix}{T_{C} = {\frac{{R_{U} \cdot w} - \gamma}{\alpha} = {{\frac{R_{U}}{\alpha} \cdot w} - \frac{\gamma}{\alpha}}}} & (14)\end{matrix}$

Similarly, by recalling that the overall resistance of the leg EG isequal to R_(U), the temperature of the hot heating element 252 _(H) canbe related to w as follows: $\begin{matrix}{T_{H} = {{\frac{R_{U}}{\alpha}\frac{w + 1}{w}} - \frac{\gamma}{\alpha}}} & (15)\end{matrix}$

by assuming that the heat transfer coefficient is similar for bothheating elements 252 _(H) and 252 _(C), Equation (9), written for bothheating elements 252 _(H) and 252 _(C), yields the following ratio:$\begin{matrix}{{\frac{w^{2}}{w + 1}\frac{\Delta \quad V_{H}^{2}}{\Delta \quad V_{C}^{2}}} = {{w + 1} = \frac{T_{H} - T_{G}}{T_{C} - T_{G}}}} & ( {16,17} )\end{matrix}$

By combining Equations (14), (15) and (17), one may obtain thetemperature of the gas as: $\begin{matrix}{T_{G} = {{\frac{R_{U}}{\alpha}( {w + 1 - {1/w} - {1/w^{2}}} )} - \frac{\gamma}{\alpha}}} & (18)\end{matrix}$

Equivalently, in the range of voltage ratio w between 1 and 1.4, whichare suggested as a result of experiments and relevant calculations, thefollowing relation approximates the expression in parenthesis with thenecessary accuracy:

g(w)=w+1−1/w−1/w ²≈2.7685w−2.6569  (19)

Consequently, Equation (18) assumes the following form: $\begin{matrix}{T_{G} = {{{2.7685\quad \frac{R_{U}}{\alpha}w} - \frac{\gamma + {2.6569\quad R_{U}}}{\alpha}} = {{A \cdot w} + B}}} & (20)\end{matrix}$

A number of important observations can be made by the analysis ofEquations (14) and (20):

From Equation (14), it is evident that, if the diameter of the heatingelement 252, if for example it is comprised of a platinum wire, ischanged from d₁ to d₂, keeping constant the length of the wire, therelationship between the temperature of the cold heating element 252_(C) and the voltage ratio does not change if the ratio R_(U)/α remainsthe same. This simplifies significantly the design process of theelectric circuit. It is possible to maintain the ratio R_(U)/α constantand the temperature of the heating elements 252 _(H) and 252 _(C) abovethe Leidenfrost transition while changing the wire diameter if theresistance R_(U), and therefore R_(BS), is changed proportionally to thetemperature coefficient α.

From Equation (20), one may notice that if the ratio R_(U)/α is notchanged while varying the wire diameter, the sensitivity of the sensorprobe 250 does not change. It is well known that the sensitivity of ameasurement device is proportional to the derivative of the calculatedquantity T_(G) with respect to the measured one w.

Therefore, it is possible to decrease the current flowing into thecircuit by simply using a thinner wire, without losing accuracy in themeasurement process and remaining above the Leidenfrost transition withboth the heating elements 252 _(H) and 252 _(C). However, otherpractical restrictions limit the choice to wire diameters that are nottoo small.

As one can see from Equation (20), the relationship between the gastemperature and the voltage ratio does not depend either on the gasvelocity or the presence of the liquid droplets in the hot gas flow, aslong as both heating elements 252 _(H) and 252 _(C) are above theLeidenfrost transition. An increase of the gas velocity translates intoan increase of the voltage applied to the bridge in such a way that allthe voltages in the bridge rise proportionally to each other. Thisexplains why the ratio w is not affected by changes in the velocity aswell as its relationship with the gas temperature. The presence ofliquid droplets causes a similar effect on the voltages of the bridge.

Since the functional shown in parenthesis on the right hand side ofEquation (20) is almost linear in the range of interest, i.e.,1.1<w<1.4, the gas temperature can be obtained as:

T _(G) =A·w+B  (21)

The value of the slope A in Equation (21) has been determinedexperimentally for a variety of conditions. Upon conducting a ratherlarge number of tests, both with and without liquid droplets, the slopeA is deemed to be consistent for all tests with a numerical value ofapproximately 990±110° C. It should be noted that A and B are numericalconstants having values that depend on the features of the specificsensor configuration such as, for example only, material, length, width,diameter, and the like, and w is the ratio of the electrical resistanceacross the second heating element, i.e., 152 _(C) and 252 _(C), at thelower temperature, i.e., T_(C), and the electrical resistance across theresistor in series with the second heating element. As such, theconstant values for A and B should be calculated based on suchcharacteristics of the sensor, which may vary depending on the intendedapplication of the sensor.

A single point calibration is used to determine the parameter B inEquation (21) and yields:

T _(G)=990 w−1060  (22)

FIG. 7 illustrates the results of a series of tests conducted under dryconditions using the sensor probe 250 and comparing the results withthose obtained using a K-type thermocouple. The range of gastemperatures investigated is between 100 and 250° C., while the gasvelocity is approximately within a 3 to 5 m/s interval. In confirmingthe effectiveness of the sensor probe 250, FIG. 12 clearly shows thatmost of the data fall within a band ±10° C. about the exact value withthe average error in the range of gas temperature between 100° C. and200° C. of 7 percent.

FIG. 8 illustrates the results of a second series of tests conductedunder wet conditions using Equation (38) based on measurements providedby the sensor probe 250. Eq. (38) is discussed below in further detail.It is important to note that the test results obtained from using thesensor 250 are compared with the gas temperature measurements obtainedfrom the independent measurement system described and illustrated belowin conjunction with FIGS. 10-13. As shown, the average error in therange of gas temperature between 100° C. and 200° C. is 5 percent. Theresults clearly demonstrate the insensitivity of the sensor probe 250 toliquid droplets and the accuracy of the gas temperature readings.

FIG. 9 illustrates the temperature of the hot heating element 252 _(H)and the temperature of the cold heating element 252 _(C) versus thetemperature of the gas. The temperature traces of the heating elements252 _(H) and 252 _(C) are linear functions of the resistance of theheating elements 252 _(H) and 252 _(C). Therefore, the linearity of thetemperature trace of the cold heating element 252 _(C) confirms theabove-provided discussions on measuring the temperature of a hot gasladen with liquid droplets is accurate.

In regards to measuring the liquid volumetric fraction of hot gas ladenwith liquid droplets, such as water droplets, the liquid dropletvolumetric fraction β can be related to the temperature differencebetween the hot-gas and the temperature T_(W) detected by a wettedsensor probe 250. The temperature T_(W) measured by a wetted sensorprobe is obtained by the sensor being at a temperature below theLeidenfrost point so the liquid droplets contact the surface of thesensor probe. Consider the steady-state energy balance written for acylinder immersed in a hot gas stream laden with liquid droplets. Allthe liquid deposited on the sensor is assumed to evaporate. This isreasonable because the droplets are sparse and the gas temperature high.Therefore, there is little chance for a significant liquid build-up onthe sensor leading to run-off or re-entrainment of the liquid in thegaseous stream.

The collection efficiency κ quantifies the number of droplets that willhit the sensor with respect to the total number of droplets that flowthrough the sensor cross sectional area, A. Under these premises, theenergy balance can be written as:

ρ_(L) AUβκΛ=Sh(T _(G) −T _(W))  (23)

Note that the temperature of the wetted sensor (or wet temperature),T_(W), can be significantly lower than the hot gas temperature, T_(G).Introducing the heat transfer correlation for a cylinder in cross-flowfor Reynolds number (U·D/ν_(G)) ranging between 40 and 1000, oneobtains: $\begin{matrix}{\beta = {0.52\quad \pi \frac{{ɛ \cdot k_{G}}\Pr^{0.37}}{\kappa \quad \rho_{L}v_{G}^{0.5}\Lambda}\frac{T_{G} - T_{W}}{\sqrt{U\quad D}}}} & (24)\end{matrix}$

The parameter ε considers the enhancement of the heat transfercoefficient due to the presence of droplets in the gaseous stream. Thisparameter is set to 2 for the conditions typical of the applicationsunder consideration. Note that the ratio of the thermal conductivity andthe square root of the kinematic viscosity is nearly constant over therange of temperatures of concern. By grouping the numerical values andthe physical properties in Eq. (24) into a quantity C, the equationbecomes: $\begin{matrix}{\beta = \frac{T_{G} - T_{W}}{C\sqrt{U\quad D}}} & (25)\end{matrix}$

The constant C is determined both analytically and experimentally basedon the characteristics of the material used for the sensor probe. Todetermine the value of C analytically, the collection efficiency, κ, isset at 0.96. In the following, C is set to 85 K s^(0.5) m⁻¹ when theliquid volumetric fraction is expressed in parts per million.

With this result, the liquid volumetric fraction can be readily obtainedonce the wet temperature, the gas temperature, and the gas velocity aremeasured. As such, one finds that: $\begin{matrix}{C = \frac{\chi}{\sqrt{U\quad D}}} & (26)\end{matrix}$

This relationship provides an independent way to evaluate theevaporative cooling constant. With this approach, the value of C is 86±7K s^(0.5) m⁻¹.

The diameter of each heating element in the sensor probe 250 influencesboth the measurement resolution and the collection efficiency κ inopposite ways. Therefore, the choice of the diameter of the cylindershould be carefully optimized in order to minimize the error related tothe temperature measurement. The gas velocity U is also necessary toobtain the volumetric fraction.

For identical flow conditions, i.e., U and β constant, the difference oftemperature is proportional to the square root of the diameter of thecylinder for each heating element of the sensor probe 250. Theexperimental results, gathered from several tests with cylinders ofdifferent outside diameter provide a slope of 0.47 that confirms thetheoretical observations. Therefore, it seems reasonable to have adiameter of the cylinder for each heating element of the sensor probe beas large as possible in order to achieve a good separation between thetwo temperatures and consequently an increased accuracy in thedetermination of the liquid volumetric fraction.

However, the diameter of the cylinder for each heating element of thesensor probe affects the collection efficiency and the time responseconstant of the sensor probe, as well. The collection efficiencyprovides a measure of the fraction of droplets that cannot avoid thecylindrical obstacle and deposit on the surface. The collectionefficiency has been calculated for a wide range of the inertia parameterZ. The parameter Z is defined as the Reynolds number (Re) for the wettedsensor times the square of the ratio of the droplet diameter and wettedsensor diameter times the ratio of the water and air densities. Theresults have been fitted analytically by the following correlation:$\begin{matrix}{\kappa = {\frac{Z^{1.08}}{Z^{1.08} + 8.80} - 0.04}} & (27)\end{matrix}$

After comparing the collection efficiency and the diameter of thecylinder for each heating element of the sensor probe 250, it should benoted that the collection efficiency approaches an asymptotic value of0.97 for small sensor diameters and the collection efficiency decreasesif the diameter of the cylinder increases.

The time constant of the wet sensor probe can be obtained from atransient lump-capacity energy equation written as: $\begin{matrix}{{\rho_{S}c_{S}V_{S}\frac{T_{S}}{t}} = {h \cdot {S( {T_{G} - T_{S}} )}}} & (28)\end{matrix}$

By introducing a heat transfer correlation, the solution of Equation(28) yields a time constant given by: $\begin{matrix}{\tau = {\frac{\rho_{S}c_{S}\nu_{G}^{0.5}}{2.08\quad k_{G}U^{0.5}\Pr^{0.37}}d^{1.5}}} & (29)\end{matrix}$

Experimental results suggest an exponent of 1.58 which is in reasonableagreement with the value of 1.5 suggested by the theory. As such, thetime constant constraint favors small sensor diameters if a fastresponse time is desirable. On the basis of the results previouslyobtained, the optimal diameter of the wet sensor can be chosen so thatthe time response is compatible with the sensor of this application.Also, the restriction to remain in the asymptotic region of the dropletcollection efficiency curve is desirable, together with the bestmeasurement accuracy possible. Note that dealing with constantcollection efficiency greatly simplifies the implementation of thetechnique.

Therefore, the liquid volumetric fraction for liquid droplets istherefore simplified as:

β=(0.012±0.001)(T _(G) −T _(W))/(UD)^(1/2)  (30)

Several experiments were performed and the measurements of the liquidvolumetric fraction obtained with an optical method were compared withthose obtained from Equation (30), measuring T_(G) with the sensor probe250 and T_(W) with the wet temperature sensor. Using the sensor probe250 provides a more precise value of the liquid volumetric fraction thanthat obtained with the optical method. Furthermore, while the opticalmethod requires steady state conditions and is based on the examinationof a statistically relevant number of picture frames, the sensor probe250 is merely limited by the response time of the sensor probe.

As stated in regards to the first embodiment of the sensor probe 150,the particular components of the controller 200 is not pertinent to anunderstanding of the controller. However, the controller 200 should beable to perform several functions in addition to being able to controltwo heating elements at the same time. For example, the controller 200should maintain, in any condition, the resistance of element EG constantand equal to the resistance of element R_(U). Aside from this, thecontroller 200 should allow for a fast and reliable acquisition of thesensor outputs.

In accordance with an embodiment of the present invention, thecontroller 200 should also be capable of providing feedback to controlthe temperature of the heating elements and to maintain the feedbackabove predetermined minimum values. The controller 200 should providefixed-point arithmetic to convert incoming voltages to temperature.

In accordance with an embodiment of the present invention, anindependent measurement system was used to validate the measurementsobtained with the sensor probe. FIGS. 10-13 illustrate an example ofsuch a measurement system. It should be noted that the illustratedsystem is merely exemplary and that the system may have numerousvariations in structure so long as the below discussed theory isapplicable.

FIG. 10 illustrates a schematic diagram of a once through circuit ductsystem 10 in which a hot gas flow is established to measure the thermalresponse of a simulated sprinkler link probe immersed therein. Forexample, the system 10 may include a square duct, such as a duct havinga 0.61 m×0.61 m cross-section, wherein the dimensions are merelyexemplary, through which a steady air flow is induced by a blower 70,such as a fan, positioned near the outlet 80.

Air entering the inlet 20 is heated by a heat source 30, such as, forexample only, a 70 kW natural gas burner, that warms up the air at theinlet. The hot gas proceeds through a honeycomb structure 40 comprising,for example only, tightly packed steel wool, positioned immediatelyadjacent the inlet 20 to obtain a uniform velocity and temperature ofthe hot gas. It is within the scope of this invention to have thehoneycomb structure 40 comprise any other suitable material so long asthe velocity and temperature of the hot gas passing through thestructure is uniform upon exiting.

As shown in FIG. 11, after passing through the honeycomb structure 40,the hot gas enters a plenum 50 having a plurality of spray nozzles 52 i,wherein i=2, 3, 4, . . . n, that add liquid to the hot gas. It is withinthe scope of this invention to have n equal the number of spray nozzlesnecessary to provide the needed spray of liquid droplets. Furthermore,it should be understood that the spray nozzles are to be chosen so as toprovide the desired amount of liquid droplets having a predetermineddroplet size distribution.

The flow of the hot gas laden with liquid droplets 51 is thenaccelerated through an orifice 60, the geometry of the orifice being anysuitable geometric shape, such as, for example only, circular,rectangular, triangular, trapezoidal, and the like. The actual geometryof the orifice is not of critical importance so long as the flow of thehot gas emerging therefrom is uniform. The cross-sectional area of theorifice 60 may be, for example only, 0.25 m in diameter and locatedapproximately 0.5 m downstream of the spray nozzles 52 i.

As shown in FIG. 12, the test section 100 is located downstream of theorifice 60 in the vena contracta and the velocity field in the testsection 60 is one-dimensional. A plurality of thermocouples arepositioned downstream of the orifice 60 to provide a description of theevolution of the temperature of the hot gas. Although differentconfigurations of the duct system 10 will yield different results,within the cross-section of the illustrated system, the temperaturevariation detected by plurality of thermocouples was determined not toexceed 8° C. in both gas and gas-liquid conditions. Furthermore, aplurality of thermocouples, such as, for example only, type K, ±2° C.,are placed inside the system 10, both before and after the test section100 so as to measure the gas temperature distribution along the duct andmonitor the conditions during the experiment. The hot gas flow is cooledby the heat transferring to the walls of the duct system and by mixingcold air drawn into the system through secondary inlets 65, as shown inFIG. 10.

With conventional methods and devices, temperature measurements, as wellas determination of other properties, of a hot gas laden with liquiddroplets are significantly affected by evaporative cooling as liquiddroplets impact, for example, the temperature sensor, or other devicebeing used to measure the property, and evaporate on its surface. Thefollowing description provides a novel approach to the measurement ofthe temperature and other properties of the hot gas. It should be notedthat one aspect of the present invention is that the sensor probe ismaintained at temperatures exceeding the Leidenfrost transition so as tobe insensitive to the presence of the liquid droplets in the hot gas.

FIG. 13 illustrates a typical temperature distribution for probes inboth dry and wet conditions performed in accordance with the test devicedescribed further below. T_(D) is a curve of the temperature of the gasas measured in a dry environment, with the data points indicated. T_(G)is the estimate of the gas temperature in wet conditions. T_(W) presentsthe data for the temperature detected by the conventional probe in wetconditions. A comparison between the values of the temperature measuredat a test section after which liquid droplets have been introducedclearly shows the effect of the evaporative cooling in wet conditions onthe wet probe.

It is worth noting that, due to the heat losses to the externalenvironment, the temperature drops as the flow proceeds downstream ofthe introduction of the gas. Furthermore, approximately 2 m downstreamthe test section indicated in the graph shown in FIG. 13, the slope ofthe temperature distribution for the wet condition nearly equals theslope for the temperature distribution for the dry condition, which isindicative of the liquid being completely evaporated and that thetemperature being affected only by the heat losses to the environment.The difference in temperature T° C. between the temperature profiles ofthe dry and wet conditions T_(D) and T_(W), respectively, a considerabledistance from the orifice of introduction of the gas can be related tothe heat required to vaporize the liquid droplets

To determine the gas temperature T_(G) between the sprays and thelocation of the complete evaporation of the liquid, some informationconcerning the rate of vaporization of the droplets is needed. Considerthe energy balance written for the air flow as:

ρ_(G){dot over (V)}_(G) c _(G)(T _(D) −T _(G))=ρ_(L) {dot over (V)}_(G)(β₀−β)Λ  (31)

Consider the asymptotic temperature difference, ΔT between the twotraces in FIG. 13, which is associated with the sensible heat removedfrom the air in order to vaporize the droplets. This difference can beexpressed in the following form: $\begin{matrix}{{\Delta \quad T} = \frac{\rho_{L}{{\overset{.}{V}}_{G} \cdot \beta_{0} \cdot \Lambda}}{\rho_{L}{\overset{.}{V}}_{G}c_{G}}} & (32)\end{matrix}$

With Eq. (32), Eq. (31) can be simplified as:

T _(D) −T _(G) =ΔT[l−f(x)]  (33)

where the function f(x) links the initial volumetric fraction to itsevolution along the duct.

The energy balance written for a thermocouple wetted by liquid dropletsyields a relation of proportionality between the convective heat inputto the thermocouple and the latent heat associated with the vaporizationof the droplets that impact over the surface of the thermocouple. Forthe purpose of measuring the gas temperature T_(G), a simple form of theenergy balance is given as:

h(T _(G) −T _(W))∝ρ_(L) UβΛ  (34)

Considering the volumetric fraction evolution during the evaporationprocess, Eq. (34) can be rearranged as:

T _(G) −T _(W)=χβ₀ f(X)  (35)

By adding Eq. (33) and Eq. (35), one finds that the functional f(x) canbe expressed in the following form: $\begin{matrix}{{f(x)} = \frac{T_{D} - T_{W} - {\Delta \quad T}}{{\chi \quad {\beta \quad}_{0}} - {\Delta \quad T}}} & (36)\end{matrix}$

It should be noted that f(x) must be equal to 1 at the spray nozzleslocation and equal to zero for x greater or equal to x_(E), a point atwhich all the liquid droplets are evaporated. A reasonablerepresentation of the data is obtained as: $\begin{matrix}{{f(x)} = \{ \begin{matrix}( {1 - \frac{x}{x_{E}}} )^{\lambda} & {x \leq x_{E}} \\{0\quad} & {x > x_{E}}\end{matrix} } & (37)\end{matrix}$

It follows that the interpolation describing the gas temperature T_(G)is given by substituting Eq. (37) into Eq. (33) to yield:$\begin{matrix}{T_{G} = {T_{D} - {\Delta \quad {T\quad\lbrack {1 - ( {1 - \frac{x}{x_{E}}} )^{\lambda}} \rbrack}}}} & (38)\end{matrix}$

the temperature in dry conditions T_(D) is represented with anexponential fit of the available data in the following form:

T _(D)=(T ₀ −D)e ^(−αx) +Bx+D  (39)

The constant B represents the slope of the trace on the right hand sidedue to the heat transfer losses to the ambient. It is reasonable topresume that this approach provides a good representation of the hot gastemperature trend. In particular, the intersection of this curve withthe vertical dashed line in FIG. 1 provides the hot gas temperature atthe test section point for liquid droplets introduced into a hot gasunder test conditions described further below. As one may notice fromthe plot, the evaporative cooling reduces the thermocouple reading ofthe wet probe by some 50° C. with respect to the estimated gastemperature T_(G).

It should also be noted that in the independent measurement system beingdescribed, the test section 100 is illuminated by a laser, such as, forexample only, a 600 mW Argon-ion laser sheet. However, it should benoted that any suitable illumination device can be used. The velocitymeasurements in the cross-section are obtained with a particle trackingvelocimetry technique that yields uncertainty in the velocitymeasurements of approximately 10 percent.

As the volumetric mean diameter of the droplets is less than 100 μm, theterminal velocity is smaller than approximately 0.14 m/s. Since the gasvelocities are in excess of 3.5 m/s, the difference between the dropletand gas velocities introduces an error of less than 4 percent in the gasvelocity measurement.

While there has been illustrated and described what is at presentconsidered to be preferred embodiments of the present invention, it willbe understood by those skilled in the art that various changes andmodifications may be made, and equivalents may be substituted forelements thereof without departing from the true scope of the invention.

For example, as shown in FIG. 14, a terminal 400 may be provided tosupport the heating elements 152 and 252 held by the rods 154 and 254.In this arrangement, the heating element 152 of 252 is placed between aclamp 401 and the rod 154 or 254. Each rod 154 or 254 has a bore 470formed therein that is sized and configured to receive a fasteningdevice 471, which is shown as a screw, but can be any known or laterdeveloped suitable device. When the threaded portion 471 b of thefastening device 471 is threadably inserted into the bore 470 of the rod154 or 254, the head portion 471 a of the fastening device 471 securesthe clamp in place and the terminal 400 prevents the heating element 152or 252 from being crushed. Thus, the mounting of the heating element 152or 252 onto the rod 154 or 254 is easier and a better match between thecopper rods and the platinum heating elements are achieved, resulting ina lower resistance of contact.

In addition, many other modifications may be made to adapt a particularsituation or material to the teachings of the invention withoutdeparting from the scope thereof. For example, although theabove-provided discussion of the present invention discussed applicationof the sensor probe in application with a simulated sprinkler link, itis in no way intended to limit the scope of the applications of thepresent invention. In particular, it is envisioned that the sensor probeincludes applications in numerous fields.

Specifically, in aerospace engineering, the sensor probe can easily findapplications in the cooling process of turbo-machinery blades and in thestudy of fuel evaporation within the combustion chamber. Likewise, inthe field of automotive engineering, the sensor probe can be used in theinvestigation of the fuel evaporation process between the point ofinjection and the engine cylinder inlet. Furthermore, in thechemical/process industry and laboratories, further applications can befound in any process where a liquid is entrained and carried by a gasflow, such as cooling towers and multiple phases mixing. Therefore, itis intended that this invention not be limited to the particularembodiment or application disclosed herein, but will include allembodiments and applications within the spirit and scope of thedisclosure.

Λ=latent heat of vaporization of water

A, B=numerical constants having values that depend upon configuration ofthe sensor probes

b=an exponent less than one

β=a liquid volumetric fraction

C=a constant

C_(G)=evaporative cooling parameter for gas

c_(s)=specific heat

d=cylinder diameter

D=an outer diameter of the wetted sensor probe

ε=a parameter that considers the enhancement of the heat transfercoefficient due to the presence of droplets in the gaseous stream

F=a coefficient that depends on the ratio of the heat transfercoefficients

f(x)=a function that links the initial volumetric fraction to itsevolution along the duct

H_(C)=the heat transfer coefficient for the cold heating element

H_(H)=the heat transfer coefficient for the hot heating element

i_(C)=the current in the cold heating element

i_(H)=the current in the hot heating element

κ=the liquid droplet collection efficiency for wet sensor

k_(G)=gas thermal conductivity

l=length of wire expressed in cm

Pr=Prandtl number

ρ_(L)=density of liquid

ρ_(s)=density of solid

Q_(C)=the power to maintain the cold heating element at the cold elementpredetermined temperature

Q_(H)=the power to maintain the hot heating element at the hot elementpredetermined temperature

R₂₀=resistance of platinum per unit length of wire, expressed in ohm/cm,at 20° C.

R_(C)=the resistance in the cold heating element

R_(H)=the resistance in the hot heating element

R_(U)=the resistance of leg EG in FIG. 5

S=heat transfer surface, m²

T_(C)=the temperature of the cold heating element

T_(H)=the temperature of the hot heating element

T_(G)=temperature of gas

T_(S)=temperature of heat transfer surface

T_(W)=a temperature measured by a wetted sensor

ΔV_(BS)=voltage change across resistor element BS in FIG. 5

ΔV_(C)=change in voltage across the cold heating element

ΔV_(EF)=voltage difference between points E and F in FIG. 5

ν_(G)=kinematic viscosity of gas

V_(G)=volumetric

V_(S)=volume of solid

ΔV_(H)=change in voltage across the hot heating element

U=a velocity of the hot gas laden with liquid droplets

w=the ratio of an electrical resistance across the second heatingelement at the second temperature to an electrical resistance across aresistor of the controller that is in series with the second heatingelement

χ=parameter in equation 5

x_(E)=a point at which all the liquid droplets are evaporated

λ=exponent of the water volumetric fraction evolution

Z=inertia parameter

We claim:
 1. A system for measuring the characteristics of a gas ladenwith droplets of a liquid, the liquid having a Leidenfrost temperature,the system comprising: a first probe maintained at a first temperatureabove the Leidenfrost temperature for the liquid; and a controllercoupled to the first probe; wherein the controller provides power tomaintain the first probe at the first temperature above the Leidenfrosttemperature for the liquid and for measuring the power provided to thefirst probe; wherein at least one parameter of the gas laden withdroplets of a liquid is known; and wherein an unknown parameter isdetermined using the measured power provided to the first probe and theat least one known parameter.
 2. The sensor probe according to claim 1,wherein a liquid volumetric fraction of the gas laden with the dropletsof the liquid is determined based on the following relationship:β=(0.012±0.001)(T _(G) −T _(W))/(U·D)^(1/2) wherein β represents theliquid volumetric fraction, T_(G) is a temperature of the gas laden withthe droplets of the liquid, T_(W) is a temperature measured by a wettedsensor, U is a velocity of the gas laden with the droplets of the liquidand D is an outer diameter of the wetted sensor.
 3. The sensor probeaccording to claim 1, wherein the Leidenfrost transition for thedroplets of the liquid is in a range between 300-350° C. at atmosphericconditions.
 4. The sensor probe according to claim 1, further comprisinga second probe maintained at a second temperature above the Leidenfrosttemperature of the liquid, wherein the first probe comprises a firstheating element and the second probe comprises a second heating element,wherein the controller controls the operation parameters of the firstand second heating elements simultaneously.
 5. The sensor probeaccording to claim 1, further comprising a second probe maintained at asecond temperature above the Leidenfrost temperature of the liquid,wherein the first probe comprises a first heating element and the secondprobe comprises a second heating element, wherein the first and secondheating elements are cylindrical.
 6. The sensor probe according to claim5, wherein the longitudinal axes of the first and second heatingelements are parallel relative to each other.
 7. The sensor probeaccording to claim 6, wherein the insulator connected to each of thefirst and second heating elements is comprised of a rigid ceramic. 8.The sensor probe according to claim 5, wherein the longitudinal axes ofthe first and second heating elements are coaxial.
 9. The sensor probeaccording to claim 8, further comprising a support frame including threebent rods connected at a first end of each rod and equidistant from eachother at a second end of each rod, wherein the second ends of the rodsare provided on line coaxial with the longitudinal axes of the first andsecond heating elements.
 10. The sensor probe according to claim 9,wherein a distance between the second ends of the rods is equal to thelength of the first and second heating elements.
 11. The sensor probeaccording to claim 10 wherein connecting means connect the first andsecond heating elements to the second ends of the rods.
 12. The sensorprobe according to claim 11 wherein the connecting means comprise a boreformed in the second end of each rod and a fastening means having athreaded portion and a head portion.
 13. The sensor probe according toclaim 12, wherein the bore is sized and configured to receive thethreaded portion of the fastening means and the head portion of thefastening means maintains the heating element against the correspondingrod.
 14. The sensor probe according to claim 12, wherein the fasteningmeans further comprise a clamp having a bore identical to the bore inthe second end of each rod and a terminal that maintains a predetermineddistance between the clamp and rod, wherein the bores are sized andconfigured to receive the threaded portion of the fastening means andthe clamp maintains the heating element against the corresponding rod.15. The sensor probe according to claim 8, wherein the first and secondheating elements comprise platinum wire.
 16. The sensor probe accordingto claim 9, wherein the support frame and connecting rods are enclosedwithin temperature-shrinking tubing.